write 1+√-32/4 as a complex number in the form a + bi, where a and b are real numbers.
a. 1/4+1/2√2i
b. 1/4+1/4√2i
c. 1/4+√2i
d. 1/4+4√2i

Answers

Answer 1
Answer: Choice C

Work Shown:

[tex]\frac{1+\sqrt{-32}}{4}\\\\\frac{1+\sqrt{-1*16*2}}{4}\\\\\frac{1+\sqrt{-1}*\sqrt{16}*\sqrt{2}}{4}\\\\\frac{1+i*4*\sqrt{2}}{4}\\\\\frac{1+4i*\sqrt{2}}{4}\\\\\frac{1}{4}+\frac{4i*\sqrt{2}}{4}\\\\\boldsymbol{\frac{1}{4}+i\sqrt{2}}\\\\[/tex]

This matches with choice C. The imaginary 'i' term is not under the square root.


Related Questions

Which pairs of figures are congruent? Which pairs are similar?


Answers

Answer: Look at the explanation

Step-by-step explanation: To understand what figures are congruent and what figures are similar, you need to understand what the terms mean.

Congruent figures have the same shape and size.

Similar figures have the same shape but different size.

The 1st figure is not congruent but it is similar.

2nd figure is congruent and similar which are rectangles. Wheather the figure is rotated or reflected, it is still congruent and similar.

3rd figure is both, congruent and similar which are both triangles.

4th figure is neither. There is a circle and an elipse, which are both round but different shapes.

By knowing the terms congruent and similar, you should have no problem in identifying geometric shapes and sizes.

Hope this helps. Happy learning!

1. Find the surface area of the pyramid to the nearest whole number.
12 m
6 m

Answers

Answer: 36m
step by step explanation below:

At Health Hair, the cost of a children's haircut, x , is $4 and the cost of an adult haircut, y , is $14. The sales from Friday were $568. There were 42 haircuts in all.

Write a system to represent the situation.

AND

Solve the system and interpret the answer.

Your Answer:

Answers

Answer:

[tex]x + y = 42,[/tex]

[tex]4x + 14y = 568,[/tex]

[tex]x = 2, y = 40[/tex]

Step-by-step explanation:

Learn the FULL explanation at: https://brainly.com/question/25629296

add the quotient of 9 and 7 to d

Answers

Answer:

9 ÷ 7 + d.

Step-by-step explanation:

Which bottle of water costs more per ounce: a 12
ounce bottle for $1.25 or a 16 ounce bottle for
$1.50?

I really need help with this!

Answers

Answer:

the second bottle

Step-by-step explanation:

To get the amount it costs per ounce, divide the amount of money by the number of ounces.

A water bottle that costs $1.25 for 12 ounces costs roughly 10 cents per ounce. A water bottle that costs about 9 cents per ounce.

therefore, the 16 ounce bottle is cheaper per ounce

Help for points and Ill give brainliest to correct!

Answers

Answer:

D. 3 1/4

Step-by-step explanation:

Answer:

your answer would be D.

Step-by-step explanation:

all you have to do for this equation is subtract the whole numbers to get 3. and then subtract the fractions, you would get 2/8, then you would simplify it and get 1/4.

Write 8% as a fraction or mixed number in simplest form.

please help me

Answers

The simplest form of fraction for 0.8 is 4/ 5.

Answer one question. Thanks

Answers

The y-intercept is 4.
Simply identify the y-intercept by looking at where the line crosses the y-axis. Or by looking at the equation (in y=mx+b form), the b term is the y-intercept.

Find the value of x ​in the given figure

Answers

Answer:

32°

Step-by-step explanation:

Its pretty strait forward.

2x + 60° + 3x - 40° = 180°

5x + 20° = 180°

5x = 160°

x = 160°/5

x = 32°

Actually I am from India, Please Mark me as brainliest.....

please answer the two question and how you answered it NO LINKS AND NO WEBSITES I really need help with tthis, and also if it's Substitution or linear combination.​

Answers

Answer:

  (x, y) = (6, 8) using linear combination

Step-by-step explanation:

The coefficients of the x-terms are opposites of each other (2 and -2), so the x-terms can be eliminated using a linear combination of the equations.

Adding the two equations together gives ...

  (2x -y) +(-2x +3y) = (4) +(12)

  2y = 16 . . . . . . . . simplify

  y = 8 . . . . . . . divide by 2

Substituting for y in the first equation gives ...

  2x -8 = 4

  x -4 = 2 . . . . . divide by 2

  x = 6 . . . . . . . add  4

The solution is (x, y) = (6, 8).

Name an angle adjacent to FGI
JGI

HGJ

DGE

HGE

Answers

Answer:<JGI

Explanation:

Any angle with the letter H can not be as it is on the opposite side. Leaving you with <JGI and <DGE. <DGE is beside angles DGF and angle EGH

Hope this helps.

The adjacent angle of the angle ∠FGI will be ∠JGI. Then the correct option is A.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

An angle is a structure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

From the figure, the contiguous point of the point ∠FGI will be ∠JGI. Then the right choice is A.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

The price of a computer is first reduced by 10% and after a while by another 20%. Who is right? Explain how you are thinking.

Almir: In total, the price has been reduced by 30%.
Bodil: The reduction is less than 30%. Viktor: The price has been reduced by more than 30%.​

Answers

if u reduced the price by 10% first it would go from 100% to 90%

20% of 90 is 18

at the end the price is 72% of the original price.

Bodil is correct. The reduction is less than 30%.

Please someone help meee! It’s advanced algebra

Answers

Answer: I think it would be 80 feet I hole I’m correct.

Step-by-step explanation: So to explain 20 + 50 is 80 and that’s how I got the answer I am not 100% sure but I wanted to help you :-)

one of 50 states is chosen at random. What is the probability of not choosing a state that begins with the letter n?

Answers

Answer:

8 states start with the letter N. Because you’re looking for the amount of states not starting with the letter N, we’ll subtract 8 from 50. Then you’ll put that over the total amount of states. So you should end up with 42/50 which will simplify to 21/25. Hope this helped!

Step-by-step explanation:

the square roots of 8 and 2

Answers

Answer:

4.82842712475

Step-by-step explanation:

hope you get it

It is 4.82842712475

I used a calculator

Find the product of (4z2 7z â€"" 8) and (â€""z 3). The product of (4z2 7z â€"" 8) and (â€""z 3) is â€""4z3 z2 z â€"" 24.

Answers

The product of both functions using the distributive law is [tex]-4z^3 + 5z^2 + 29z - 24[/tex]

We are to find the product of (4z^2+7x-8) and (-z+3)

Product  =  (4z^2+7z-8)(-z+3)

Using the distributive law:

[tex]P =4z^2(-z) + 4z^2(3) + 7z(-z) +7z(3)-8(-z) -8(3)\\P = -4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24\\P = -4z^3 + 5z^2 + 29z - 24[/tex]

Hence the product of both functions using the distributive law is [tex]-4z^3 + 5z^2 + 29z - 24[/tex]

Learn more on product of functions here: https://brainly.com/question/25638609

Someone please help this is soooooo hard

Answers

Step-by-step explanation:

1. 10x-7=5x+3; ⇒ 5x=10; ⇒ x=2. If x=2, then

2. QS=10*2-7=14;

3. SR=5*2+3=13;

4. m(∠PSR)=15*2+42=72°;

5. m(∠PSQ)=180-m∠(PSR)=180-72=108°.

simplify 4 (5x+3)-4x

Answers

Answer:

16x + 12

Step-by-step explanation:

20x + 12 - 4x

20x - 4x = 16x

16x + 12

Answer: 15x + 12

Step-by-step explanation:

(4 x 5x). (4 x 3). (20x - 4x). 15x + 12 is your answer.

Here ya go bestie. Your favorite :D

Answers

Answer:

the answer is d

Step-by-step explanation:

22. A company's stock price dropped $10 a week for one year. How much will it have decreased by the end of the year? ​

Answers

I think it’s 520 $10 times the amount of weeks in a year

The difference of x and 15 is 62. Solve for x

Answers

Answer:

x is either 77 or -47

Step-by-step explanation:

Answer: either 77 or -47

Step-by-step explanation:

please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Joe purchases a tray of 48 flowers to plant in his garden. He plants 3 flowers every minute. He can plant the entire tray in 16 minutes.

When setting up a graph to model how many flowers he plants over time, what would be an appropriate scale for the x-axis (horizontal axis)?

Question 10 options:

0 - 48


0 - 3


16 - 48


0 - 16

Answers

Answer:

B im very sorry if im wrong <3

Step-by-step explanation:

Answer:48

Step-by-step explanation:Required equation is y - 36 = (24 - 36)/(2 - 1) (x - 1)

y - 36 = -12(x - 1)

y - 36 = -12x + 12

12x + y = 12 + 36

12x + y = 48

Choose the point-slope form of the equation below that
epresents the line that passes through the points (-6, 4) and (2,
0). (2 points)

•y -4= - 1/2 (x+6)

•y-4= 2(x+6)

•y+6= - 1/2(x-4)

•y+6= 2(x-4)

Answers

Answer:

A) y-4=-1/2(x+6)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-4)/(2-(-6))

m=-4/(2+6)

m=-4/8

simplify

m=-1/2

y-y1=m(x-x1)

y-4=-1/2(x-(-6))

y-4=-1/2(x+6)

what number is 100`000 more than seven hundred two thousand eight three

Answers

Answer:

802,083

Step-by-step explanation:

If Mrs. Hill takes out a mortgage for $80,000 with a 4% interest rate, what will her interest be after 20 years? Help ASAP I’ll give so much points!

Answers

Answer:

After 20 years, Mrs. Hill is owed $144,000.

Step-by-step explanation:

Using PRT/100, we can find the interest Mr. Hill has to pay extra.=> 80000 x 4 x 20/100=> 800 x 4 x 20=> 3200 x 20=> 64000Total amount to pay: $144,000

Conclusion:

Therefore, after 20 years, Mrs. Hill is owed:

$144,000.

Hoped this helped.

[tex]GeniusUSer[/tex]

Find the area of a garden with a length of 3 1/2 yards and a width of 2 2/3 yards

Answers

Answer:

2.33 yards

Step-by-step explanation:

3 1/2-3.5

2/3-0.66

0.66 x 3.5 = n

0.737 ___ 0.708
0.708 > 0.737
0.737 = 0.708
0.737 < 0.708
0.737 > 0.708

Answers

Answer:

0.737>0.708

Step-by-step explanation:

it must me d because 0.737 is greater than 0.708 and it's the only true Statement

Solve for xx. Leave your answer in simplest radical form.

Answers

Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

does anyone know how to do this?

Answers

Answer:

x = 1y = -7

Step-by-step explanation:

The coefficients of x and y do not have any "nice" relations, so doing this by elimination is just "brute force" with no particular subtlety.

After multiplying by appropriate numbers, you want the coefficient of one of the variables in one equation to be the opposite of the coefficient of the same variable in the other equation. Here, we can get that by multiplying the first equation by 7 and the second equation by 2.

  7(2x +3y = -19)   ⇒   14x +21y = -133

  2(-7x +2y = -21)   ⇒   -14x +4y = -42

Adding these equations with opposite x-coefficients eliminates the x-terms. (That is how the "elimination" method gets its name.)

  (14x +21y) +(-14x +4y) = (-133) +(-42)

  25y = -175 . . . . . . . . simplify

  y = -7 . . . . . . . . . . . divide by 25

Substituting this value into the first equation gives ...

  2x +3(-7) = -19

  2x = 2 . . . . . . . . . add 21

  x = 1 . . . . . . . . . divide by 2

The solution is x = 1, y = -7.

_____

Additional comment

The multipliers used in this process are essentially the coefficients of one of the variables, with one of them negated. Here, we chose the x-coefficients, because negating one of them gives two positive multipliers. We judge it easier to do the arithmetic using positive numbers.

Had we chosen to use the y-coefficients (3 and 2) for our multipliers, we would probably multiply the first equation by 2, and the second equation by -3. That way, the remaining x-coefficient would be positive.

Planning ahead is helpful, but not essential. It can help to avoid errors and make the work easier to do.

Do it quickly please for brainliest

Answers

Step-by-step explanation:

x/(2x - 4) - (2x - 11)/(x + 2) = 5/8x/(x - 2) - (4x - 22)/(x + 2) = 5/4x(x + 2) - (4x - 22)(x - 2) = 5/4(x + 2)(x - 2)4(x² + 2x - 4x² + 8x + 22x - 44) = 5(x² - 4)4(-3x² + 32x - 44) = 5x² - 20- 12x² + 128x - 176 - 5x² + 20 = 0- 17x² + 128x - 156 = 017x² - 128x + 156 = 0x = (64 ± 38)/17x = 6 or x = 26/17

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